Real world: NFL player value in the 2018 season

Value in the real world

At the most general level, a player’s value is determined by their contribution to a team’s performances vs. their cost to a team. A $1 million quarterback who contributes a certain amount to his team’s success is more valuable than a $10 million quarterback who contributes an equivalent amount, because his lower salary leaves room for investing in the rest of the team. While it makes sense for teams to pay top-dollar for top-level talents, good teams are after value: securing the best contributions for the lowest price.

Visualizing value

I used the plotly library to produce the interactive plots below. Hovering over each point will reveal that player’s DYAR and cap hit for the 2018 season (you can also drag a box over a region on each plot you want to zoom in on).

The plots include regression lines capturing the relationship between players’ cap hits and their DYAR. For quarterbacks (QB), cap hit accounts for 22% of the variation in DYAR. For wide receivers (WR), cap hit accounts for 12% of the variation. (By social science standards, these are pretty large effects). For tight ends (TE), cap hit accounts for 5% of the variation; smaller but still statistically significant. In other words, more costly players at these positions tend to contribute more on average.

However, for running backs (RB), cap hit only accounts for less than 1% of the variation and this relationship is not statistically significant. Consistent with the aforementioned take that running backs lack value, teams are able to get good production out of even cheaper running backs.

Players higher up on the y-axis contributed more DYAR, and players furter to the right on the x-axis had larger cap hits. In each plot, I have included red lines indicating the average cap hit and DYAR by position.

Players in the upper left quadrants possessed the best value – their cap hits were less than average, and they produced above average DYAR. Examples of these were TE George Kittle and QB Patrick Mahomes, who gained the most DYAR at their respective positions in 2018 on relatively low cap hits. Players in the lower right quadrant had the worst value. For example, RB LeSean McCoy had the highest cap hit at his position, and actually produced -134 DYAR (he contributed way less than an average RB).

Value rankings

The plots above are pretty useful for spotting outliers, but it’s difficult to compare the relative value of players that appear close together. For each position, the following tables display the relative value of the most active players (I excluded players that played very little). Value is computed as the DYAR gained per $1,000 of that player’s cap hit.²

The tables are ordered to display players with the highest value first. Click on the DYAR per $1,000 column to reverse the order and view the least valuable players. You can also sort by other variables like cap hit, touches, and DYAR.

Where to find value

From the plots above, it’s clear that great players don’t necessarily cost a team an arm and a leg. This has led to the rise in the present strategy of building a team around a quarterback on a rookie contract. Because quarterbacks command the largest contracts later on, having even a slightly above average quarterback for cheap provides ample resources for the rest of a team’s roster.

However, it does make sense to pay good quarterbacks and wide receivers (and to a lesser degree, tight ends) to keep them, as established players at those position are likelier to outperform cheaper ones. In contrast, there doesn’t seem to be anything about a running back’s price that predicts his performance. The present aversion to paying running backs seems pretty rational, as even a cheap running back could lead to above average production.